A254005 Numbers that divide the reverse of the sum of their aliquot parts.

1, 6, 2274, 44304, 229974, 498906, 4177662, 20671542, 22999974, 41673714, 73687923, 403999652, 479444901, 4158499614, 27378395352, 209659386726, 216276435966, 229999999974, 406406685462, 922964834547

Offset: 1

Author

Paolo P. Lava, Jan 22 2015

Keywords

• nonn
• base
• more

Comments

Noting 2274, 229974, and 22999974, 23*10^n-26 is a term herein for any n in A253968. - Hans Havermann, Jan 24 2015

Additionally, 404*10^(6*n)-348 is a term herein if this is 28 times a prime. Three such numbers are known: n = 1, 10, and 1608. - Hans Havermann, Jan 28 2015

a(21) > 10^12. - Giovanni Resta, May 09 2015

Examples

			sigma(1) - 1 = 0, Rev(0) = 0 and 0 / 1 = 0.
sigma(6) - 6 = 6, Rev(6) = 6 and 6 / 6 = 1.
sigma(2274) - 2274 = 2286, Rev(2286) = 6822 and 6822 / 2274 = 3.
		

Crossrefs

Cf. A000203, A001065, A253968, A254004.

Programs

Magma

[n: n in [1..10^7] | Seqint(Reverse(Intseq(SumOfDivisors(n)-n))) mod n eq 0]; // Vincenzo Librandi, May 09 2015

Maple

with(numtheory): T:=proc(w) local x,y,z; x:=w; y:=0;
for z from 1 to ilog10(x)+1 do y:=10*y+(x mod 10); x:=trunc(x/10);
od; y; end:
P:=proc(q) local n; for n from 1 to q do
if type(T(sigma(n)-n)/n,integer) then print(n);
fi; od; end: P(10^9);

Mathematica

fQ[n_] := Mod[ FromDigits@ Reverse@ IntegerDigits[ DivisorSigma[1, n] - n], n] == 0; k = 1; lst = {}; While[k < 1000000001, If[fQ@ k, AppendTo[lst, k]]; k++]; lst (* Robert G. Wilson v, Jan 28 2015 *)

PARI

rev(n) = subst(Polrev(digits(n)), x, 10);
isok(n) = rev(sigma(n)-n) % n == 0; \\ Michel Marcus, Jan 25 2015

Extensions

More terms from Hans Havermann, Jan 24 2015

a(13) from Robert G. Wilson v, Jan 29 2015

a(14)-a(20) from Giovanni Resta, May 09 2015